Mayo equation

With the omission of the reinitiation reaction, this scheme is the same as that for polymerization with chain transfer and an expression (eq 28) for the degree of polymerization similar in form to the Mayo equation can be derived. 

This equation (eq. 5) is commonly known as the Mayo equation.1" The equation is applicable at low (zero) conversion and is invalidated if the rate constants are chain length dependent. 

The most used method is based on application of the Mayo equation (eq. 5). For low (zero) conversion polymerizations carried out in the presence of added transfer agent T, it follows from eq. 5 that a plot of 1/ Xn vs [T]0/[M]0 should yield a straight line with slope Clr.12 Thus, a typical experimental procedure involves evaluation of the degree of polymerization for low conversion polymerizations earned out in the presence of several concentrations of added transfer agent. The usual way of obtaining Xn values is by GPC analysis of the entire molecular weight distribution. 

A number of authors have provided integrated forms of the Mayo equation, 2"w which have application when the conversion of monomer to polymer is non-zero. Integration of eq. 12 provides eq. 15 ... 

Nair et a/." 7 have proposed a modified Mayo equation for use when retardation through primary radical termination with transfer agent-derived radicals is significant. 

This section concerns studies directed toward an elucidation of relative rate constants, k,./kp and kt/kp, and a mechanistic interpretation of these parameters. The data for the HMWF of PIB samples prepared with 7-BuCl and f-BuBr/Et2AlCl/MeCl systems shown in Table 7 were calculated from Mayo plots (see also p. 56 for Mayo Equation) using M data given in Tables 4 and 5. The data of LMWF of PIB prepared with f-BuBr/Et2AlCl/MeCl system at —50 °C shown in Table 7 were calculated from Mayo plots using M data given in Table 5. 

Mayo plot provides relative rate constants of the molecular weight controlling events22. Transfer and/or termination with solvent, polymer and impurities are assumed to be negligible. Although the Mayo equation is strictly valid only for data obtained at low conversion, Plesch23 has shown that the plot provides remarkably reliable information even with data obtained at relatively high conversions. 

If the very small term in kt is dropped, the Mayo equation (iii) can now be written in the... 

The same form of rate equation and Mayo equation can also be obtained, though with different constants, on the assumption, made by Biddulph and Plesch when first discussing this work [77], that the chain breaking agent is the stannic chloride hydrate itself. Since this reaction too would be subject to deceleration by increasing viscosity, it is also compatible with the curves of Figure 9. 

The DPs obtained in polymerisations catalysed by SnCl4-CCl3C02H, with [SnCl4]/ [CC13C02H] 3-4, [SnClJ = (23-36) x 10 3 mole/l, at -20°, -50°, and -78° in w-hexane, chloroform, and methylene dichloride were studied by Imanishi, Higashimura, and Okamura [79]. They interpreted the results in terms of the Mayo equation in the form,... 

The DP of the polymers. The variation of the DP with [H20] at T - -13° is shown in Figure 17 and similar curves were obtained at other temperatures. The DP was completely independent of [TiCl4] the variation of DP with monomer concentration obeyed the Mayo equation down to -50°, but at -60° and -90° the DP was independent of monomer concentration down to... 

The Mayo equation for these reactions thus has the form... 

Amongst several other innovations there is here a demonstration of how the Mayo plots can reveal the kinetic order of a polymerisation with respect to the monomer. Another timely advance is the generalisation of the Mayo equation for the case of a dieidic polymerisation by unpaired and paired cations. This development was taken further in a very useful review that can be considered to be a follow-up or progress report from the work under discussion here (B). 

If it is assumed that the dissociation constant, Ky, of the ion pairs is independent of the length of the polymer chain attached to the cation, the Mayo equation takes the form... 

As far as the DP is concerned, the author s finding that its dependence on [thiophene] obeys the Mayo equation shows that equation (27) is the appropriate one. However, it follows from this that on our interpretation the slope of the Mayo plot is not, as the... 

My idea that in bulk monomer and in some solutions the propagation is a unimolecular reaction is supported strongly by the way in which the DP depends on the monomer concentration. At low m, 1/DP increases rectilinearly with 1/m, as demanded by the conventional Mayo equation for bimolecular propagation but at high m, 1/DP increases rectilinearly with m, as is required for unimolecular propagation (see Section 5). 

The inversion of (5.9) yields (5.10), which resembles the conventional Mayo equation, except that it contains the c ... 

One of the most characteristic and common features of cationic polymerisation is that, as the concentration of one of the components of the reaction mixture is changed, the degree of polymerisation (DP) of the polymers varies in a manner such that the relevant curve shows a more or less abrupt, sometimes even catastrophic, change of direction and cannot be represented simply by the Mayo equation. 

If F, G, and H (or substances originating directly from them) are (potential) chain-breakers, the DP will be governed by a Mayo equation of the form ... 

The tables include only those systems in which the DP variation shows a turning point or discontinuity, so that it must be classed as abnormal and is not amenable to analysis by the simple Mayo equation. It is, of course, impossible to discuss each in detail and those selected for such treatment in the following pages are marked in the tables by an asterisk. 

The concentrations of both chain transfer agent and initiator are important for the polymerization when the concentration of HPMA is constant. The molecular weight of the ST HPMA polymers was regulated by the concentration ratio of mercaptan (S) to HPMA (M), according to the Mayo equation, lT>P (end) = + Q[S]/[M] [27]. DP (end) are the num-... 

The Mayo equation (Equation 6.42) that gives positive slopes when the data is plotted (such as Figure 6.3) is the reciprocal relationship derived from the expression cited earlier. The ratio of the rate of cessation or termination by transfer to the rate of propagation is called the chain transfer constant (Cs). 

When disproportionation is important, this can be taken into account by reverting back to Eq. 3-105 to derive the most general form of the Mayo equation ... 

The use of the Mayo equation (Eq. 3-108 in its various forms) allows one to quantitiatively determine the effects of normal termination and transfer to monomer, initiator, and solvent on the molecular weight of the product and then adjust the reaction parameters to obtain the desired molecular weight. Two cases are encountered. 

Case 1 involves a reaction system that yields a molecular weight lower than needed. One analyzes the different terms on the right side of the Mayo equation to determine which one(s) is (are) responsible for the low molecular weight and the reaction parameters are then adjusted accordingly to increase the molecular weight. The initiation rate would be lowered if the low molecular weight is due to an excessively high initiation rate. If the initiator or... 

To describe the composition of copolymers which are polymerized at a given mole ratio of the comonomers, the well known Mayo equation (II) is used ... 

In evaluating these measurements the Mayo equation 5 is used. This is also done in two other publications (5, 27). This equation cannot be used in its strictest sense, as noted previously. However, by appropriate... 

Except for small deviations the r2 values correspond with the values obtained using the Mayo equation 5. The ri values have been fitted to the experimental data by trial and error and are tabulated in Table IV. The calculated curves as well as the measured points are plotted in Figure 4. The measured points and the calculated curves are in good agreement at low temperature—i.e., 20°-80°C however at 100°C deviations become apparent. 

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